A recent survey revealed that 54% of 18-to-34 year olds, 33% of 35-to-54 year olds, and 15% of those ages 55+ use YouTube to listen to music.
If 10 people ages 35 to 54 are randomly selected, find the probability that no less than 8 use YouTube to listen to music. answer in 4 decimals

We are given that 33% (or \( p = 0.33 \)) of people aged 35 to 54 use YouTube to listen to music. We need to find the probability that at least 8 out of 10 randomly selected people in this age group use YouTube to listen to music. This is a binomial probability problem.

The binomial probability formula is:

\[
P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k}
\]

Where:
- \( n = 10 \) (the number of trials, or the number of people selected),
- \( k \) is the number of successes (we are looking for \( X \geq 8 \)),
- \( p = 0.33 \) (the probability of success on a single trial),
- \( 1 - p = 0.67 \) (the probability of failure on a single trial).

To solve the problem, we want to find:

\[
P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)
\]

We will calculate these probabilities individually using the binomial formula and sum them up.

Let me calculate this.The probability that no less than 8 out of 10 randomly selected people aged 35 to 54 use YouTube to listen to music is approximately **0.0032** (rounded to 4 decimal places).

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the probability that exactly 5 out of 10 people use YouTube to listen to music?
2. How would the result change if we surveyed 20 people instead of 10?
3. What is the expected number of people using YouTube out of 10?
4. How do we calculate the variance in this binomial distribution?
5. How would the probability change if the percentage of users increased to 50%?

**Tip:** In binomial probability problems, the sum of probabilities for all possible outcomes (0 to \(n\)) always equals 1.

A recent survey revealed that 54% of 18-to-34 year olds, 33% of 35-to-54 year olds, and 15% of those ages 55+ use YouTube to listen to music. If 10 people ages 35 to 54 are randomly selected, find the probability that no less than 8 use YouTube to listen to music. Answer in 4 decimals.

Find the probability that no less than 8 out of 10 randomly selected people aged 35 to 54 use YouTube to listen to music. This problem explores binomial probability with a 33% success rate, focusing on calculating probabilities for a range of outcomes. Suitable for students in Grades 10-12.

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